Module 12 Test Review: Radical Expressions and Equations

Name _______________________________________ Date __________________ Class __________________

Module 12 Test Review: Radical Expressions and Equations

For 1¨C3, translate the expression with

rational exponents into a radical

expression and simplify, if possible.

1. y

8.

? ?32?

3

________________________________________

7

4

9. The annual rate of inflation, in percent, of

a home that increases in value from p to

q over a period of n years is

_______________________________________

? 243 ?

2. ? ?

?

? 32 ?

5

1

2

5

? q ?n

I ? 100 ? ? ? 100. Find the annual rate

?p?

of inflation, to the nearest tenth of a

percent, of a home that doubles in value

over 20 years.

_______________________________________

3. (81)0.75

________________________________________

_______________________________________

10. Is each expression equivalent to

1.5

4. Is each expression equivalent to 0.36 ?

A 0.36

2

3

C

?

0.36

?

Yes

No

Yes

No

Yes

No

B ? ? ? ? ??

Yes

No

C

Yes

No

A

E

0.363

D

? 4? ?

3

Yes

No

s

n

t

Yes

No

? ?

s ?n t

Yes

No

Yes

No

For 11¨C16, simplify the expression.

Assume that all variables are positive. All

exponents should be positive in simplified

form. Rationalize any irrational

denominators.

3

_______________________________________

7.

No

1

n

n

Yes

1

m9

6

1

n

? s? n

E ? ?

?t?

_______________________________________

6.

?

1

For 5¨C8, translate the radical expression

into an expression with rational exponents

and simplify, if possible.

5.

sn

t

2

3

D 0.36 2

s

?

t

1

B 0.216

3

n

? 53

8

11. ?? 7

? 89

?

85

3

?4

?

?

?

?

_______________________________________

________________________________________

Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

59

Name _______________________________________ Date __________________ Class __________________

? 32 ?

5a b ?

12. ??

7 ?

? 6b 5 ?

?

?

2

________________________________________

20.

_______________________________________

4

3

4x ? 1 ? ?5

________________________________________

x5y 3

13.

3x ? 13 ? x ? 5

19.

x2y 5

21.

________________________________________

_______________________________________

6

3

?3x ? 11 ? x ? 3

14. ¡Ì5 ? ¡Ì25 ? ¡Ì1252

1

22. 2 ? x ? 2? 3 ? x ? 2

_______________________________________

________________________________________

15.

3

21m

3

7m 2 n

2

23. Choose True or False for each statement

1

about the equation ? x ? 14 ? 2 ? x ? 2.

_______________________________________

3

16.

A It has one solution.

True

3

¡Ì4 ? ¡Ì80

3

B It has two solutions.

¡Ì5

True

_______________________________________

False

C It has one extraneous solution.

17. The surface area S of a sphere as a

function of its volume V is given by

True

False

D It has two extraneous solutions.

2

3

? 3V ?

S ? 4? ?

? . Rewrite the expression for

? 4? ?

the surface area as the product of a

simplified coefficient term and a variable

term using only positive exponents. Then

write the approximate formula with the

coefficient term rounded to the nearest

thousandth.

True

False

E It has no solutions.

True

False

3

24. The equation ? + 6400 = ¡Ì1.3 ¡Á 1011 ? ? 2

relates the distance d in kilometers of a

certain GPS satellite above the surface of

the Earth to the number of hours t it takes

the satellite to complete one orbit. The

average distance of this satellite above the

surface of the Earth is 20,100 kilometers.

To the nearest hour, how long does it

take the GPS satellite to complete one

orbit of the Earth?

_______________________________________

For 18¨C22, solve each equation. Identify

any extraneous roots.

1

18.

False

? x ? 3?2 ? 1 ? x

_________________________________

_______________________________________

Original content Copyright ? by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.

60

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